A NOTE ON PERFECT ORDERED SPACES

By a linearly ordered topological space CLOTS) we mean a linearly ordered set equipped with the usual open interval topology of the given order. By a generalized ordered space (GO-space) we mean a linearly ordered set equipped with a Tl-topology for which there is a base of order convex sets [L]. To say that a topological space is perfect means that every closed subset of the space is a Go-set. Finally, for any space X, the set of non-isolated dpoints of X is denoted by x • In abstract spaces, the property of being perfect has little relationship to other familiar properties. This contrasts with th ~ situation in ordered spaces where, for example, it is known that a separable GO-space must be perfect, and a perfect GO-space must be paracompact [BLl) [EL). In [vW], van Wouwe sharpened that first implicatio